There are a few differences in the democrats and republicans. They are focused mainly on responsibilities of government, taxation and economic stimulus, focus on where our resources need to be spent, and how trade should be approached in relation to US interest. Other social issues have been tied to certain parties such as abortion, environment, gun control to name a few. The social issues are mainly for debate purposes in the legislative branches because within both parties you will find division in these areas. I know democrats who are pro-life and I know republicans who believe in strict gun control.
As to roles of government, and this is very plain to see between the parties, the republicans believe in very little responsibility of the government to interfere with the daily lives of the people. So since the government can do so little, it should be allowed to do what little it can without question. The democrats believe that the government has an obligation to insure its citizens are safe and to do this the government has much power to do what ever it wants. So since the government has so much power, it must have a bunch of hoops and hurdles to go through to make sure the people are safe guarded from abuse from the government. A prime example of this today is the wire tap debate.
Taxation and economic stimulus is a HUGE difference between the parties. This is where you hear republicans are for big business and the democrats are for the working man. The republicans in this department go for the trickledown theory which says that if you give tax breaks to the rich then you have reinvestment in the company and inovative technology research. Both of which lead to new market shares and thus new jobs for the American citizen. Better products for better prices comes from research and the company having money to burn on experiments. Basically the market leads the consumer.
The democrats believe that the tax breaks need to go to the working class or trickle up if you will. Since there are so many more of them they determine what innovations need to be made. With so many people with extra money are out there, better products for better prices comes from competition since the companies must produce to get the consumer. Innovation comes from what the buying public says it wants. New jobs for US citizens comes from increased demand on the best goods that people want. The consumer leads the market.
Also on taxation and role of government. The republicans are big on rugged individualism and free market. They believe that if you want services you should go out and pay for them yourself, in return taxes will be lower. The democrats believe that the citizens have a right to want certain services from their government, but they better be ready to pay taxes to get them.
But shoot, its getting late and I could go a long time on the different philosophies of the parties. In truth neither is 100% right or 100% wrong. Both have there places and in my opinion, it is where the country is at a certain time as to who gets into power.
Independents are normally someone who really hasn't tied themselves to any party and ran on their own accord. When they vote though, most show either republican or democratic values.